// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// package math -- go2cs converted at 2022 March 13 05:42:03 UTC
// import "math" ==> using math = go.math_package
// Original source: C:\Program Files\Go\src\math\log1p.go
namespace go;

public static partial class math_package {

// The original C code, the long comment, and the constants
// below are from FreeBSD's /usr/src/lib/msun/src/s_log1p.c
// and came with this notice. The go code is a simplified
// version of the original C.
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
//
// double log1p(double x)
//
// Method :
//   1. Argument Reduction: find k and f such that
//                      1+x = 2**k * (1+f),
//         where  sqrt(2)/2 < 1+f < sqrt(2) .
//
//      Note. If k=0, then f=x is exact. However, if k!=0, then f
//      may not be representable exactly. In that case, a correction
//      term is need. Let u=1+x rounded. Let c = (1+x)-u, then
//      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
//      and add back the correction term c/u.
//      (Note: when x > 2**53, one can simply return log(x))
//
//   2. Approximation of log1p(f).
//      Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
//               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
//               = 2s + s*R
//      We use a special Reme algorithm on [0,0.1716] to generate
//      a polynomial of degree 14 to approximate R The maximum error
//      of this polynomial approximation is bounded by 2**-58.45. In
//      other words,
//                      2      4      6      8      10      12      14
//          R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s  +Lp6*s  +Lp7*s
//      (the values of Lp1 to Lp7 are listed in the program)
//      and
//          |      2          14          |     -58.45
//          | Lp1*s +...+Lp7*s    -  R(z) | <= 2
//          |                             |
//      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
//      In order to guarantee error in log below 1ulp, we compute log
//      by
//              log1p(f) = f - (hfsq - s*(hfsq+R)).
//
//   3. Finally, log1p(x) = k*ln2 + log1p(f).
//                        = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
//      Here ln2 is split into two floating point number:
//                   ln2_hi + ln2_lo,
//      where n*ln2_hi is always exact for |n| < 2000.
//
// Special cases:
//      log1p(x) is NaN with signal if x < -1 (including -INF) ;
//      log1p(+INF) is +INF; log1p(-1) is -INF with signal;
//      log1p(NaN) is that NaN with no signal.
//
// Accuracy:
//      according to an error analysis, the error is always less than
//      1 ulp (unit in the last place).
//
// Constants:
// The hexadecimal values are the intended ones for the following
// constants. The decimal values may be used, provided that the
// compiler will convert from decimal to binary accurately enough
// to produce the hexadecimal values shown.
//
// Note: Assuming log() return accurate answer, the following
//       algorithm can be used to compute log1p(x) to within a few ULP:
//
//              u = 1+x;
//              if(u==1.0) return x ; else
//                         return log(u)*(x/(u-1.0));
//
//       See HP-15C Advanced Functions Handbook, p.193.

// Log1p returns the natural logarithm of 1 plus its argument x.
// It is more accurate than Log(1 + x) when x is near zero.
//
// Special cases are:
//    Log1p(+Inf) = +Inf
//    Log1p(±0) = ±0
//    Log1p(-1) = -Inf
//    Log1p(x < -1) = NaN
//    Log1p(NaN) = NaN
public static double Log1p(double x) {
    if (haveArchLog1p) {
        return archLog1p(x);
    }
    return log1p(x);
}

private static double log1p(double x) {
    const float Sqrt2M1 = 4.142135623730950488017e-01F; // Sqrt(2)-1 = 0x3fda827999fcef34
    const float Sqrt2HalfM1 = -2.928932188134524755992e-01F; // Sqrt(2)/2-1 = 0xbfd2bec333018866
    const float Small = 1.0F / (1 << 29); // 2**-29 = 0x3e20000000000000
    const float Tiny = 1.0F / (1 << 54); // 2**-54
    const nint Two53 = 1 << 53; // 2**53
    const float Ln2Hi = 6.93147180369123816490e-01F; // 3fe62e42fee00000
    const float Ln2Lo = 1.90821492927058770002e-10F; // 3dea39ef35793c76
    const float Lp1 = 6.666666666666735130e-01F; // 3FE5555555555593
    const float Lp2 = 3.999999999940941908e-01F; // 3FD999999997FA04
    const float Lp3 = 2.857142874366239149e-01F; // 3FD2492494229359
    const float Lp4 = 2.222219843214978396e-01F; // 3FCC71C51D8E78AF
    const float Lp5 = 1.818357216161805012e-01F; // 3FC7466496CB03DE
    const float Lp6 = 1.531383769920937332e-01F; // 3FC39A09D078C69F
    const float Lp7 = 1.479819860511658591e-01F; // 3FC2F112DF3E5244 

    // special cases

    if (x < -1 || IsNaN(x)) // includes -Inf
        return NaN();
    else if (x == -1) 
        return Inf(-1);
    else if (IsInf(x, 1)) 
        return Inf(1);
        var absx = Abs(x);

    double f = default;
    ulong iu = default;
    nint k = 1;
    if (absx < Sqrt2M1) { //  |x| < Sqrt(2)-1
        if (absx < Small) { // |x| < 2**-29
            if (absx < Tiny) { // |x| < 2**-54
                return x;
            }
            return x - x * x * 0.5F;
        }
        if (x > Sqrt2HalfM1) { // Sqrt(2)/2-1 < x
            // (Sqrt(2)/2-1) < x < (Sqrt(2)-1)
            k = 0;
            f = x;
            iu = 1;
        }
    }
    double c = default;
    if (k != 0) {
        double u = default;
        if (absx < Two53) { // 1<<53
            u = 1.0F + x;
            iu = Float64bits(u);
            k = int((iu >> 52) - 1023); 
            // correction term
            if (k > 0) {
                c = 1.0F - (u - x);
            }
            else
 {
                c = x - (u - 1.0F);
            }
            c /= u;
        }
        else
 {
            u = x;
            iu = Float64bits(u);
            k = int((iu >> 52) - 1023);
            c = 0;
        }
        iu &= 0x000fffffffffffff;
        if (iu < 0x0006a09e667f3bcd) { // mantissa of Sqrt(2)
            u = Float64frombits(iu | 0x3ff0000000000000); // normalize u
        }
        else
 {
            k++;
            u = Float64frombits(iu | 0x3fe0000000000000); // normalize u/2
            iu = (0x0010000000000000 - iu) >> 2;
        }
        f = u - 1.0F; // Sqrt(2)/2 < u < Sqrt(2)
    }
    float hfsq = 0.5F * f * f;
    double s = default;    double R = default;    double z = default;

    if (iu == 0) { // |f| < 2**-20
        if (f == 0) {
            if (k == 0) {
                return 0;
            }
            c += float64(k) * Ln2Lo;
            return float64(k) * Ln2Hi + c;
        }
        R = hfsq * (1.0F - 0.66666666666666666F * f); // avoid division
        if (k == 0) {
            return f - R;
        }
        return float64(k) * Ln2Hi - ((R - (float64(k) * Ln2Lo + c)) - f);
    }
    s = f / (2.0F + f);
    z = s * s;
    R = z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 + z * (Lp6 + z * Lp7))))));
    if (k == 0) {
        return f - (hfsq - s * (hfsq + R));
    }
    return float64(k) * Ln2Hi - ((hfsq - (s * (hfsq + R) + (float64(k) * Ln2Lo + c))) - f);
}

} // end math_package
